Angela Merkel has agreed EU leaders should formally vote on whether to make Jean-Claude Juncker president of the commission if consensus cannot be reached, according to Downing Street.

The German chancellor made the commitment during a phone call with David Cameron ahead of a crunch summit this week.

The Prime Minister has insisted he will keep on fighting "until the end" in a bid to prevent Mr Juncker getting the EU's top job, arguing it should go to a more reform-minded candidate.

However, Mr Cameron is expected to be heavily outnumbered at the gathering in Brussels tomorrow and Friday, and Liberal Democrat colleague Vince Cable earlier criticised his approach as undermining Britain's influence in the union.

A Number 10 spokeswoman said Mr Cameron took calls from Mrs Merkel and Dutch counterpart Mark Rutte this afternoon.

"The Prime Minister explained that his opposition to the 'Spitzenkandidaten' process would not change," the spokeswoman said.

"Chancellor Merkel and Prime Minister Rutte recognised the PM's position and agreed that if the European Council decides not to proceed by consensus then there should be a vote.

"Both leaders also underlined their support for Britain's continued membership of a reformed European Union and their ongoing commitment to working with the Prime Minister as he renegotiates Britain's relationship with the EU."

Mr Cameron believes that the selection of a candidate chosen by the largest party grouping in the European Parliament would breach the principle that candidates for top jobs are nominated by national leaders and not by MEPs.

But he has seemingly failed to recruit enough allies to block the appointment at the summit under qualified majority voting (QMV) rules.

Questions had also been raised as to whether he would be able to push the matter to a formal vote, or whether Council president Herman van Rompuy would allow it to be "nodded through".

Mr Juncker has said he is confident of securing the post by the end of this week, "if common sense prevails".

In an apparent dig at the Prime Minister's campaign against him, the former Luxembourg premier said he was being forced to wait for a decision because common sense was "very unequally distributed".

Mr Cable told the BBC Radio 4 Today programme earlier that Mr Cameron was " right in principle that the appointment of the commission president shouldn't be foisted on heads of government".

But he added: "I think he was right to take the position he did but the way it's been done, unfortunately, has not helped Britain punch its weight in Europe."